Technically no, but depending on how you use your browser, you might see one default location when you are signed into your Yahoo! account, and another default location when you are signed out.

The default location that is associated with your Yahoo! account remains the same unless you change it, and you can have only one default associated with your Yahoo! account at a time.

It is also possible to set a default location when you are signed out, This default location is unrelated to your Yahoo! ID and is set to expire if you do not select it during a 90-day period.